Financial Mathematics  Please can any one help me to solve this problem?
Mathematics

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Attached is the detailed solution in excel Repayment.xlsx
Here is the method for your reference 
1. We need to find a value of P for which the total amount of 40,000 gets repaid under given conditions. Therefore
Present value (PV) = 40000
Future value (FV) = 0 (to repay all)
Time period = 12*5 = 60
2. I have used the discounting formula to find out the present value of all future payments and equated it to 40,000. Then I have found out for what value of P this equation holds true.
Answer: P = 4640.025
Let me know if you need further help
Thank you for your prompt response.
I have a question please clarify, why you used "i"  Interest value as is which is 12%, while in problem it says, nominal interest rate of 12% compounded monthly. Does this mean that, we have to determine the monthly effective interest, which will equal to 12/12=1% !!!
Please answer.
I have use total number of periods = 60 which is to say I have considered each month as an individual payment period. Thus it is perfectly okay to use 12% and there is NO NEED to find effective rate.
Don't get confused with notations. In this solution, a month is a period with 12% interest rates.
I got your point.
Why I am asking, because, I need to submit the solution, and show the approach i used, I mean I must use the "formula" , when I am using formula, I was considering monthly effective interest as 1% in the "Increasing AnnuityImmediate Present Value"..
If I want to use your figures, which formula I will have to use, if we want to solve it other than excel?
The way I solve such questions is to assume a random value for payment P to begin with, find the sum of PV of all payments and then use Goal seek tool of excel to find exact value of P.
If we look at formula based approach then we have to go for 'Annuities whose payments follow an arithmetic progression'. There is a paper which explains this technique, if you want I will share the link with you, but it is not my work.
Attached is the formula for the same taken from third party paper inc annuity 1.png
Let me know if you want me to share the link of the paper with you.
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